Particle transport in open polygonal billiards: A scattering map.

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2024-12-01 DOI:10.1063/5.0219730
Jordan Orchard, Federico Frascoli, Lamberto Rondoni, Carlos Mejía-Monasterio
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引用次数: 0

Abstract

Polygonal billiards exhibit a rich and complex dynamical behavior. In recent years, polygonal billiards have attracted much attention due to their application in the understanding of anomalous transport, but also at the fundamental level, due to their connections with diverse fields in mathematics. We explore this complexity and its consequences on the properties of particle transport in infinitely long channels made of the repetitions of an elementary open polygonal cell. Borrowing ideas from the Zemlyakov-Katok construction, we construct an interval exchange transformation classified by the singular directions of the discontinuities of the billiard flow over the translation surface associated with the elementary cell. From this, we derive an exact expression of a scattering map of the cell connecting the outgoing flow of trajectories with the unconstrained incoming flow. The scattering map is defined over a partition of the coordinate space, characterized by different families of trajectories. Furthermore, we obtain an analytical expression for the average speed of propagation of ballistic modes, describing with high accuracy the speed of propagation of ballistic fronts appearing in the tails of the distribution of the particle displacement. The symbolic hierarchy of the trajectories forming these ballistic fronts is also discussed.

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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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